I support this, especially because I had a friend dump a pet on me and then leave and it's really awkward to have. Definitely an event with the pet's name, like someone said above

Couldn't this be a separate page under Adopt R Us?

Like the page where we have all our gifts listed, but with pets. That way we could just get an alert to visit that page and then see what it was all about.

Sign the paperwork and get your new pet - or refuse and let the owner deal with it.